166 lines
4.5 KiB
Idris
166 lines
4.5 KiB
Idris
module Data.Profunctor.Yoneda
|
|
|
|
import Data.Profunctor
|
|
import Data.Profunctor.Costrong
|
|
import Data.Profunctor.Traversing
|
|
import Data.Profunctor.Mapping
|
|
import Data.Profunctor.Sieve
|
|
|
|
%default total
|
|
|
|
|
|
------------------------------------------------------------------------------
|
|
-- Yoneda
|
|
------------------------------------------------------------------------------
|
|
|
|
|
|
||| The cofree profunctor given a data constructor with two type parameters.
|
|
public export
|
|
record Yoneda p a b where
|
|
constructor MkYoneda
|
|
runYoneda : forall x, y. (x -> a) -> (b -> y) -> p x y
|
|
|
|
export
|
|
Profunctor (Yoneda p) where
|
|
lmap f (MkYoneda p) = MkYoneda $ \l,r => p (f . l) r
|
|
rmap f (MkYoneda p) = MkYoneda $ \l,r => p l (r . f)
|
|
dimap f g (MkYoneda p) = MkYoneda $ \l,r => p (f . l) (r . g)
|
|
|
|
export
|
|
ProfunctorFunctor Yoneda where
|
|
promap f (MkYoneda p) = MkYoneda $ f .: p
|
|
|
|
export
|
|
ProfunctorMonad Yoneda where
|
|
propure p = MkYoneda $ \l,r => dimap l r p
|
|
projoin (MkYoneda p) = p id id
|
|
|
|
export
|
|
ProfunctorComonad Yoneda where
|
|
proextract (MkYoneda p) = p id id
|
|
produplicate p = MkYoneda $ \l,r => dimap l r p
|
|
|
|
||| A witness that `Yoneda p` and `p` are equivalent when `p` is a profunctor.
|
|
export
|
|
yonedaEqv : Profunctor p => p a b <=> Yoneda p a b
|
|
yonedaEqv = MkEquivalence propure proextract
|
|
|
|
export
|
|
yonedaIso : (Profunctor q, Profunctor r) => forall p. Profunctor p =>
|
|
p (q a b) (r a' b') -> p (Yoneda q a b) (Yoneda r a' b')
|
|
yonedaIso = dimap proextract propure
|
|
|
|
export
|
|
Functor (Yoneda p a) where
|
|
map = rmap
|
|
|
|
export
|
|
GenStrong ten p => GenStrong ten (Yoneda p) where
|
|
strongl = propure . strongl {ten,p} . proextract
|
|
strongr = propure . strongr {ten,p} . proextract
|
|
|
|
export
|
|
GenCostrong ten p => GenCostrong ten (Yoneda p) where
|
|
costrongl = propure . costrongl {ten,p} . proextract
|
|
costrongr = propure . costrongr {ten,p} . proextract
|
|
|
|
export
|
|
Closed p => Closed (Yoneda p) where
|
|
closed = propure . closed . proextract
|
|
|
|
export
|
|
Traversing p => Traversing (Yoneda p) where
|
|
traverse' = propure . traverse' . proextract
|
|
wander f = propure . wander f . proextract
|
|
|
|
export
|
|
Mapping p => Mapping (Yoneda p) where
|
|
map' = propure . map' . proextract
|
|
roam f = propure . roam f . proextract
|
|
|
|
export
|
|
Sieve p f => Sieve (Yoneda p) f where
|
|
sieve = sieve . proextract
|
|
|
|
export
|
|
Cosieve p f => Cosieve (Yoneda p) f where
|
|
cosieve = cosieve . proextract
|
|
|
|
|
|
------------------------------------------------------------------------------
|
|
-- Coyoneda
|
|
------------------------------------------------------------------------------
|
|
|
|
|
|
||| The free profunctor given a data constructor with two type parameters.
|
|
public export
|
|
data Coyoneda : (p : Type -> Type -> Type) -> Type -> Type -> Type where
|
|
MkCoyoneda : (a -> x) -> (y -> b) -> p x y -> Coyoneda p a b
|
|
|
|
|
|
export
|
|
Profunctor (Coyoneda p) where
|
|
lmap f (MkCoyoneda l r p) = MkCoyoneda (l . f) r p
|
|
rmap f (MkCoyoneda l r p) = MkCoyoneda l (f . r) p
|
|
dimap f g (MkCoyoneda l r p) = MkCoyoneda (l . f) (g . r) p
|
|
|
|
export
|
|
ProfunctorFunctor Coyoneda where
|
|
promap f (MkCoyoneda l r p) = MkCoyoneda l r (f p)
|
|
|
|
export
|
|
ProfunctorMonad Coyoneda where
|
|
propure = MkCoyoneda id id
|
|
projoin (MkCoyoneda l r p) = dimap l r p
|
|
|
|
export
|
|
ProfunctorComonad Coyoneda where
|
|
proextract (MkCoyoneda l r p) = dimap l r p
|
|
produplicate = MkCoyoneda id id
|
|
|
|
||| A witness that `Coyoneda p` and `p` are equivalent when `p` is a profunctor.
|
|
export
|
|
coyonedaEqv : Profunctor p => p a b <=> Coyoneda p a b
|
|
coyonedaEqv = MkEquivalence propure proextract
|
|
|
|
export
|
|
coyonedaIso : (Profunctor q, Profunctor r) => forall p. Profunctor p =>
|
|
p (q a b) (r a' b') -> p (Coyoneda q a b) (Coyoneda r a' b')
|
|
coyonedaIso = dimap proextract propure
|
|
|
|
export
|
|
Functor (Coyoneda p a) where
|
|
map = rmap
|
|
|
|
export
|
|
GenStrong ten p => GenStrong ten (Coyoneda p) where
|
|
strongl = propure . strongl {ten,p} . proextract
|
|
strongr = propure . strongr {ten,p} . proextract
|
|
|
|
export
|
|
GenCostrong ten p => GenCostrong ten (Coyoneda p) where
|
|
costrongl = propure . costrongl {ten,p} . proextract
|
|
costrongr = propure . costrongr {ten,p} . proextract
|
|
|
|
export
|
|
Closed p => Closed (Coyoneda p) where
|
|
closed = propure . closed . proextract
|
|
|
|
export
|
|
Traversing p => Traversing (Coyoneda p) where
|
|
traverse' = propure . traverse' . proextract
|
|
wander f = propure . wander f . proextract
|
|
|
|
export
|
|
Mapping p => Mapping (Coyoneda p) where
|
|
map' = propure . map' . proextract
|
|
roam f = propure . roam f . proextract
|
|
|
|
export
|
|
Sieve p f => Sieve (Coyoneda p) f where
|
|
sieve = sieve . proextract
|
|
|
|
export
|
|
Cosieve p f => Cosieve (Coyoneda p) f where
|
|
cosieve = cosieve . proextract
|